I haven’t checked the code but I think the avatar is baked into the cooked post, so those posts will have the old avatar until/unless the post is rebaked.
I have hundreds (thousands) of posts here, if changing my avatar rebaked them all, I could cause a bunch of server activity by continually changing my avatar.
Also, this is sort of a feature. This way, the post records who you were when you posted, not who you are today.